Question C3 (15% of total marks)

Two players are involved in a game. In the game each player begins with $10. Each player must simultaneously make a choice of how much of the $10 to allocate between two accounts: a 'private' account, and a 'public' account. Money allocated to the private account by a player is kept by that player. Money allocated to the public account is multiplied by 1.5, and then distributed back equally to each of the two players. Each player has two possible choices: (i) Allocate $0 to the public account; (ii) Allocate $10 to the public account. A player's payoff from each outcome is equal to the sum of their private account money and onehalf of the total public account money. For example, if both players allocated $10 to the public account, they each have a payoff equal to $0 + (1/2)($20)(1.5) = $15.00.

a) (3 marks) Draw a game table to represent this game.

b) (3 marks) Do players have a strict dominant strategy in this game?

c) (2 marks) What is the Nash equilibrium of the game?

d) (2 mark) Does the Nash equilibrium outcome maximise the total payoff to players? How can you explain this result?

Now suppose that the game is played sequentially. One player chooses which amount to allocate to the public account; after which the other player, having observed the choice made by the first player, makes their own choice of how much to allocate to the public account.

e) (3 marks) Draw the game tree for the sequential game.

f) (2 marks) What is the rollback equilibrium of the sequential game?